Inelastic scattering cross section of neutrons in displacive ferroelectrics, 2

An expression is obtained for the one-phonon differential scattering cross section of neutrons in displacive ferroelectrics in the presence of external electric field by considering higher order anharmonic terms in the Hamiltonian using the approach of I. At any temperature well above the Curie temperature T sub(c), the expression gives the field dependence as K1+K2E2, K1 and K2 being the temperature dependent anharmonic coefficients, while in the absence of external field the expression reduces to give the temperature dependence as C1T+C2T2, which is in agreement with the dependence derived in I. However in the vicinity of T sub(c), it is the long wavelength Cochran modes which give the anomalous behaviour of the scattering cross section. Electric field dependence of the square of the soft mode frequency is also discussed. It is seen that it increases with the applied field, which is in agreement with the experimental results of Worlock and Fleury. (auth.)